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[1]
Abadi, M. and Galves, A.
Inequalities for the occurrence times of rare events in mixing processes. The state of the art
Markov proc. Relat. Fields, 7(1):97-112, 2001.
[2]
Cénac, P.
On the convergence of moments in the almost sure central limit theorem for stochastic approximation algorithms
ESAIM Probability and Statistics, 17:179-194, 2013.
[3]
Arnaudon, Marc and Dombry, Clément and Phan, Anthony and Yang, Le
Stochastic algorithms for computing means of probability measures
Stochastic Process. Appl., 122(4):1437--1455, 2012.
[4]
Atlagh, M. and Weber, M.
Le théorème central limite presque sûr
Expo. Math., 18(2):97--126, 2000.
[5]
Bercu, B. and Cénac, P. and Fayolle, G.
Convergence des moments dans le théorème de la limite centrale presque sûr pour les martingales vectorielles
Rapport de recherche INRIA, 6056, 2006. 24 pages.
[6]
Bercu, B. and Cénac, P. and Fayolle, G.
On the Almost Sure Central Limit Theorem for Vector Martingales: Convergence of Moments and Statistical Applications
Journal of Applied Probability, 46:151-169, 2009.
[7]
Belfadli, R. and Es-Sebaiy, K. and Ouknine, Y.
Parameter Estimation for Fractional Ornstein-Uhlenbeck Processes: Non-Ergodic Case.
Frontiers in Science and Engineering, 1(1):1--16, 2011.
[8]
Bercu, Bernard and Nourdin, Ivan and Taqqu, Murad S.
Almost sure central limit theorems on the Wiener space
Stochastic Process. Appl., 120(9):1607--1628, 2010.
[9]
Baraud, Y. and Huet, S. and Laurent, B.
Adaptive tests of linear hypotheses by model selection
Ann. Statist., 31(1):225--251, 2003.
[10]
Bercu, B. and Fort, J.-C.
A moment approach for the almost sure central limit theorem for martingales
Studia Scientiarum Mathematicarum Hungarica, 2006.
[11]
Berkes, I.
Results and problems related to the pointwise central limit theorem
Asymptotic methods in probability and statistics (Ottawa, ON, 1997), North-Holland, Amsterdam, 1998.
[12]
Berkes, I. and Csáki, E.
A universal result in almost sure central limit theory
Stochastic Process. Appl., 94(1):105--134, 2001.
[13]
Bercu, B.
On the convergence of moments in the almost sure central limit theorem for martingales with statistical applications
Stochastic Processes and their applications, 111:157-173, 2004.
[14]
Bercu, B.
Weighted estimation and tracking for ARMAX models
SIAM J. Control Optimization, 33(1):89-106, 1995.
[15]
Blom, G. and Thorburn, D.
How many random digits are required until given sequences are obtained ?
Journal of Applied Probabilities, 19:518-531, 1982.
[16]
Bottou, L.
Large-scale machine learning with stochastic gradient descent.
Lechevallier, Y., Saporta, G. (Eds.), Compstat 2010. Physica Verlag, 2010.
[17]
Brosamler, G. A.
An almost everywhere central limit theorem
Math. Proc. Cambridge Philos. Soc., 104(3):561--574, 1988.
[18]
Bühlmann, P. and Wyner, A.J.
Variable length Markov chains
Ann. Statist., 27(2):480-513, 1999.
[19]
Cénac, P. and Chauvin, B. and Herrmann, S. and Vallois, P.
Persistent random walks, variable length Markov chains and piecewise deterministic Markov processes
Markov Processes and Related Fields, 19(1):1-50, 2013.
[20]
Cardot, H. and Cénac, P. and Monnez, J-M.
A fast and recursive algorithm for clustering large datasets with $k$-medians
Computational Statistics & Data Analysis, 56(6):1434-1449, 2012.
[21]
Cénac, P. and Chauvin, B. and Pouyanne, N. and Ginouillac, S.
Digital Search Trees and Chaos Game Representation
ESAIM Probability and Statistics, 13:15-37, 2009.
[22]
Cénac, P. and Chauvin, B. and Pouyanne, N. and Ginouillac, S.
Digital Search Trees and Chaos Game Representation
Rapport de recherche INRIA(5856), 2006.
[23]
Cénac, P. and Chauvin, B. and Paccaut, F. and Pouyanne, N.
Context trees, variable length Markov chains and dynamical sources
Séminaire de Probabilités, XLIV, 2012.
[24]
Cénac, P. and Chauvin, B. and Paccaut, F. and Pouyanne, N.
Uncommon Suffix Tries
A paraître dans Random Structures and Algorithms, 2013.
[25]
Cardot, H. and Cénac, P. and Zitt, P-A.
Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm.
Bernoulli, 19(1):18--43, 2013.
[26]
Cardot, H. and Cénac, P. and Zitt,P.-A.
Recursive estimation of the conditional geometric median in Hilbert spaces
Electron. J. Statist., 6:2535-2562, 2012.
[27]
Cénac, P. and Es-Sebaiy, K.
Almost sure central limit theorems for random ratios and applications to LSE for fractional Ornstein-Uhlenbeck processes
Non encore publié. 15 pages.
[28]
Cénac, P. and Fayolle, G. and Lasgouttes, J.-M.
Dynamical Systems in the Analysis of Biological Sequences
Rapport de recherche INRIA, 5351, 2004. 47 pages.
[29]
Clément, J. and Flajolet, P. and Vallée, B.
Dynamical sources in information theory: a general analysis of trie structures
Algorithmica, 29(1-2):307--369, 2001. Average-case analysis of algorithms (Princeton, NJ, 1998).
[30]
Cénac, P. and Loisel, S. and Maume-Deschamps, V. and Prieur, C.
Risk Indicators with several lines of business: comparison, asymptotic behavior and applications to optimal reserve allocation
Non encore publié. 21 pages.
[31]
Chaâbane, F. and Maâouia, F.
Théorèmes limites avec poids pour les martingales vectorielles
ESAIM Probab. Statist., 4:137--189 (electronic), 2000.
[32]
Cénac, P. and Maume-Deschamps, V. and Prieur, C.
Some multivariate risk indicators; Minimization by using a Kiefer-Wolfowitz approach to the mirror stochastic algorithm
Statistics and Risk Modeling, 29:47-71, 2012.
[33]
Cessac, B.
A discrete time neural network model with spiking neurons: II: Dynamics with noise
J. Math. Biol., 62(6):863--900, 2011.
[34]
Chaâbane, F. and Maâouia, F. and Touati, A.
Généralisation du théorème de la limite centrale presque-sûr pour les martingales vectorielles
C. R. Acad. Sci. Paris Sér. I Math., 326(2):229--232, 1998.
[35]
Chaâbane, F.
Invariance principles with logarithmic averaging for martingales
Studia Sci. Math. Hungar., 37(1-2):21--52, 2001.
[36]
Chaâbane, F.
Version forte du théorème de la limite centrale fonctionnel pour les martingales
C. R. Acad. Sci. Paris Sér. I Math., 323(2):195--198, 1996.
[37]
Clément, J. and Flajolet, P. and Vallée, B.
Dynamical sources in Information Theory: Analysis of general tries
Algorithmica, 29:307-369, 2001.
[38]
Comets, F. and Fernandez, R. and Ferrari, P.
Processes with long memory: Regenerative construction and perfect simulation
Ann. of Appl. Prob., 12(3):921-943, 2002.
[39]
Cardot, H. and Cénac, P. and Chaouch, M.
Stochastic approximation to the multivariate and the functional median
COMPSTAT 2010, , Paris, France., 2010.
[40]
Duflo, M. and Senoussi, R. and Touati, A.
Propriétés asymptotiques presque sûres de l'estimateur des moindres carrés d'un modèle autoregressif vectoriel
Ann. Inst. Henri Poincaré, 27(1):1-25, 1991.
[41]
Robin, S. and Daudin, J.J.
Exact distribution of word occurences in a random sequence of letters
J. Appl. Prob., 36:179-193, 1999.
[42]
Davis, M. H. A.
Piecewise-deterministic Markov processes: a general class of nondiffusion stochastic models
J. Roy. Statist. Soc. Ser. B, 46(3):353--388, 1984. With discussion.
[43]
Davis, M. H. A.
Markov models and optimization
Chapman & Hall, London, 1993.
[44]
Deschavanne, P.J. and Giron, A. and Vilain, J. and Fagot, G. and Fertil B.
Genomic Signature: Characterization and Classification of species Assessed by Chaos Game Representation of sequences
Mol. Bio. Evol., 16:1391-1399, 1999.
[45]
Devroye, L. and Neininger, R.
Random suffix search trees
Random Structures Algorithms, 23(4):357--396, 2003.
[46]
Devroye, L. and Szpankowski, W. and Rais, B.
A note on the height of suffix trees
SIAM J. Comput., 21(1):48--53, 1992.
[47]
Flajolet, P. and Sedgewick, R.
Analytic Combinatorics
Cambridge University Press, Cambridge, 2009.
[48]
Fathallah, Hamdi and Kebaier, Ahmed
Weighted limit theorems for continuous-time vector martingales with explosive and mixed growth
Stoch. Anal. Appl., 30(2):238--257, 2012.
[49]
Fayolle, J.
Compression de données sans perte et combinatoire analytique
Phd thesis, Université Paris VI, 2006.
[50]
Feller, W.
An introduction to probability theory and its applications
John Wiley, New York, 1966.
[51]
Forgy, E.
Cluster analysis of multivariate data: efficiency vs. interpretability of classifications.
Biometrics, 21:768-769, 1965.
[52]
Fredkin, Edward
Trie memory
Commun. ACM, 3(9):490--499, 1960.
[53]
Fu, J.C.
Bounds for reliability of large consecutive-$K$-out-of-$N:F$ system
IEEE trans. Reliability, 35:316-319, 1986.
[54]
Fu, J.C. and Koutras, M.V.
Distribution theory of runs: a Markov chain approach
J. Amer. Statist. Soc., 89:1050-1058, 1994.
[55]
Galvès, A. and Löcherbach, E.
Infinite systems of interacting chains with memory of variable length - a stochastic model for biological neural nets
Journal of Statistical Physics, 151(5):896--921, June 2013.
[56]
Goodwin, G.C. and Sin, K.S.
Adaptative Filtering Prediction and Control.
Prentice-Hall, Englewood Cliffs, N.J., 1984.
[57]
Gallo, S. and Garcia, N.
Perfect simulation for stochastic chains of infinite memory: relaxing the continuity assumptions
arXiv:1105.5459v1:1-20, 2010.
[58]
Galvès, A. and Löcherbach, E.
Stochastic chains with memory of variable length
TICSP Series, 38:117-133, 2008.
[59]
Gan, Guojun and Ma, Chaoqun and Wu, Jianhong
Data clustering
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2007. Theory, algorithms, and applications.
[60]
Gervini, Daniel
Robust functional estimation using the median and spherical principal components
Biometrika, 95(3):587--600, 2008.
[61]
Gerber, H. and Li, S.
The occurrence of sequence patterns in repeated experiments and hitting times in a Markov chain
Stochastic Processes and their Applications, 11:101-108, 1981.
[62]
Gonchigdanzan, K.
Almost Sure Central Limit Theorems
Phd thesis, University of Cincinnati, 2001.
[63]
Gower, J.-C.
Algorithm as 78: The mediancentre.
ournal of the Royal Statistical Society. Series C (Applied Statistics), 23(3):466--470, 1974.
[64]
Guo, L.
{Self-convergence of weighted least-squares with applications to stochastic adaptive control}
IEEE Trans. Automatic Control, 41(1):79-89, 1996.
[65]
Gusfield, D.
Algorithm on Strings, Trees, and Sequences: Computer Science and Computational Biology
Cambridge Press, 1997.
[66]
Hu, Yaozhong and Nualart, David
Parameter estimation for fractional Ornstein-Uhlenbeck processes
Statist. Probab. Lett., 80(11-12):1030--1038, 2010.
[67]
Harris, T.E.
On chains of infinite order
Pacific J. Math., 5:707-724, 1955.
[68]
Herrmann, S. and Vallois, P.
From persistent random walk to the telegraph noise
Stoch. Dyn., 10(2):161--196, 2010.
[69]
Holzmann, H. and Koch, S. and Min, A.
Almost sure limit theorems for $U$-statistics
Statist. Probab. Lett., 69(3):261--269, 2004.
[70]
Ibragimov, I. A. and Lifshits, M. A.
On limit theorems of ``almost sure'' type
Teor. Veroyatnost. i Primenen., 44(2):328--350, 1999.
[71]
Ibragimov, Ildar and Lifshits, Mikhail
On the convergence of generalized moments in almost sure central limit theorem
Statist. Probab. Lett., 40(4):343--351, 1998.
[72]
Isola, S.
Renewal sequences and intermittency
J. Statist. Phys., 97(1-2):263-280, 1999.
[73]
Jain, A. and Marty, M. and Flynn, P.
Data clustering: a review.
ACM Computing surveys, 31:264--323, 1999.
[74]
Juditsky, A. and Rigollet, P. and Tsybakov, A. B.
Learning by mirror averaging
Ann. Statist., 36(5):2183--2206, 2008.
[75]
Jeffrey, H.J.
Chaos Game Representation of gene structure
Nucleic Acid. Res, 18:2163-2170, 1990.
[76]
Karlin, S. and Burge, C.
Dinucleotide relative abundance extremes: a genomic signature
Trends Genet., 7:283-290, 1995.
[77]
Karlin, S. and Cardon, L.R.
Computational DNA Analysis
Annu. Rev. Microbiol., 48:619-654, 1994.
[78]
Karlin, S. and Landunga, I. and Blaisdell, B.E.
Heterogeneity of genomes : measures and values
Proc Natl Acad Sci USA, 91:12837-12841, 1994.
[79]
Karlin, S. and Mràzek, J.
Strand compositional asymmetry in bacterial and large viral genomes
Proc. Natl. Acad. Sci. USA, 95:3720-3725, 1998.
[80]
Karlin, S. and Mràzek, J. and Campbell, A.M.
Compositional biases of bacterial genomes and evolutionary implications
J. Bacteriol., 179(12):3899-3913, 1997.
[81]
Kaufman, Leonard and Rousseeuw, Peter J.
Finding groups in data
John Wiley & Sons Inc., New York, 1990. An introduction to cluster analysis, A Wiley-Interscience Publication.
[82]
Kiefer, J. and Wolfowitz, J.
Stochastic estimation of the maximum of a regression function
Ann. Math. Statistics, 23:462--466, 1952.
[83]
Karlin, S. and Mràzek, J.
Compositional differences within and between eukaryotic genomes
Proc. Natl. Acad. Sci. USA, 94:10227-10232, 1997.
[84]
Kemperman, J. H. B.
The median of a finite measure on a Banach space
Statistical data analysis based on the $L\sb 1$-norm and related methods (Neuchâtel, 1987), North-Holland, Amsterdam, 1987.
[85]
Koutras, M. V.
Waiting times and number of appearances of events in a sequence of discrete random variables
Advances in combinatorial methods and applications to probability and statistics, Birkhäuser Boston, Boston, MA, 1997.
[86]
Koval, V. and Schwabe, R.
Exact bounds for the rate of convergence of stochastic approximation procedures
Stochastic Anal. Appl., 16:501-515, 1998.
[87]
H. J. Kushner and D. S. Clark
Stochastic Approximation Methods for Constrained and Unconstrained Systems
Springer-Verlag, Berlin, 1978.
[88]
Lacey, M.
Laws of the iterated logarithm for partial sum processes indexed by functions
J. Theoret. Probab., 2(3):377--398, 1989.
[89]
Lai, T.L. and Wei, C.Z.
Asymptotic properties of general autoregressive models and strong consistency of least-squares estimates of their parameters
Journal of Multivariate Analysis, 13:1-23, 1983.
[90]
Lai, T.L. and Wei, C.Z.
Least-squares estimates in stochastic regression models with applications to identification and control of dynamic systems
The Annals of Statistics, 10(1):154-166, 1982.
[91]
Laloë, T.
$L_1$-quantization and clustering in Banach spaces
Math. Methods Statist., 19(2):136--150, 2010.
[92]
Lamberton, Damien and Pagès, Gilles
Recursive computation of the invariant distribution of a diffusion
Bernoulli, 8(3):367--405, 2002.
[93]
Lamberton, Damien and Pagès, Gilles
Recursive computation of the invariant distribution of a diffusion: the case of a weakly mean reverting drift
Stoch. Dyn., 3(4):435--451, 2003.
[94]
Lan, Guanghui
An optimal method for stochastic composite optimization
Math. Program., 133(1-2, Ser. A):365--397, 2012.
[95]
Lévy, P.
Théorie de l'addition des variables aléatoires
Gauthiers-Villars., 1937.
[96]
Li, S.-Y. R.
A martingale approach to the study of occurrence of sequence patterns in repeated experiments
Ann. Probab., 8(6):1171--1176, 1980.
[97]
Lifshits, M. A.
Lecture Notes on Almost Sure Limit Theorems
Publications IRMA, 54:1-25, 2001.
[98]
Lifshits, M. A.
Almost sure limit theorem for martingales
Limit theorems in probability and statistics, Vol. II (Balatonlelle, 1999), János Bolyai Math. Soc., Budapest, 2002.
[99]
MacQueen, J.
Some methods for classification and analysis of multivariate observations
Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), Univ. California Press, Berkeley, Calif., 1967.
[100]
Mahmoud, H.
Evolution of Random Search Trees
John Wiley, New York, 1992.
[101]
Pelletier, M.
On the almost sure asymptotic behaviour of stochastic algorithms
Stochastic processes and their applications, 78:217-244, 1998.
[102]
Mokkadem, A. and Pelletier, M.
A companion for the Kiefer-Wolfowitz-Blum stochastic approximation algorithm
The Annals of Statistics, 2007.
[103]
Pelletier, M.
An almost sure central limit theorem for stochastic approximation algorithms
J. Multivariate Anal., 71:76--93, 1999.
[104]
Duflo, M.
Random Iterative Methods
Springer-Verlag, 1997.
[105]
Bercu, B. and Duflo, M.
Moindres carrés pondérés et poursuite
Ann. Inst. Henri Poincaré, 28(3):403-430, 1992.
[106]
Cénac, P.
Almost sure properties of Weighted Martingales Transforms with applications to Prediction for Linear Regression Models
Probability and Mathematical Statistics, 23(1):61-76, 2003.
[107]
Martinez, H. M.
An efficient method for finding repeats in molecular sequences
nucacires, 11(13):4629--4634, 1983.
[108]
Min, A.
Limit theorems for statistical functionals with applications to dimension estimation
Phd thesis, Institute of Mathematical Stochastics, University of Göttingen, Germany, 2004.
[109]
Mokkadem, Abdelkader and Pelletier, Mariane and Slaoui, Yousri
Revisiting Révész's stochastic approximation method for the estimation of a regression function
ALEA Lat. Am. J. Probab. Math. Stat., 6:63--114, 2009.
[110]
Möttönen, Jyrki and Nordhausen, Klaus and Oja, Hannu
Asymptotic theory of the spatial median
Nonparametrics and robustness in modern statistical inference and time series analysis: a Festschrift in honor of Professor Jana Jurečková, Inst. Math. Statist., Beachwood, OH, 2010.
[111]
Nourdin, I. and Peccati, G.
Universal Gaussian fluctuations of non-Hermitian matrix ensembles: from weak convergence to almost sure CLTs
ALEA Lat. Am. J. Probab. Math. Stat., 7:341--375, 2010.
[112]
Nemirovsky, A. S. and Yudin, D. B.
Problem complexity and method efficiency in optimization
John Wiley & Sons Inc., New York, 1983. Translated from the Russian and with a preface by E. R. Dawson, Wiley-Interscience Series in Discrete Mathematics.
[113]
Nemirovsky, A. and Juditsky, A. and Lan, G. and Shapiro, A.
Robust stochastic approximation to stochastic programming
SIAM, Journal on Optimization, 19:1574-1609, 2009.
[114]
Nesterov, Y.
Primal-dual subgradient methods for convex problems
Mathematical Programming, 120:221-259, 2006.
[115]
Pagès, Gilles
A space quantization method for numerical integration
J. Comput. Appl. Math., 89(1):1--38, 1998.
[116]
Pittel, B.
Asymptotic growth of a class of random trees
Annals Probab., 13:414-427, 1985.
[117]
Polyak, B.T. and Juditsky, A.B.
Acceleration of Stochastic Approximation.
SIAM J. Control and Optimization, 30:838-855, 1992.
[118]
Pozdnyakov, V. and Glaz, J. and Kulldorff, M. and Steele, J. M.
A martingale approach to scan statistics
Ann. Inst. Statist. Math., 57(1):21--37, 2005.
[119]
Régnier, M.
A unified approach to word occurrence probabilities
Discrete Applied Mathematics, 104:259-280, 2000.
[120]
Rissanen, J.
A universal data compression system
IEEE Trans. Inform. Theory, 29(5):656-664, 1983.
[121]
Robbins, H. and Monro, S.
A stochastic approximation method
Ann. Math. Statistics, 22:400--407, 1951.
[122]
Stefanov, V. and Pakes, A. G.
Explicit distributional results in pattern formation
Annals of Applied Probabilities, 7:666-678, 1997.
[123]
Schatte, P.
On strong versions of the central limit theorem
Math. Nachr., 137:249--256, 1988.
[124]
Schatte, P.
On the central limit theorem with almost sure convergence
Probab. Math. Statist., 11(2):237--246 (1991), 1990.
[125]
Reinert, G. and Schbath, S. and Waterman, M.S.
Probabilistic and Statistical Properties of Words: An Overview
Journal of Computational Biology, 7(1/2):1-46, 2000.
[126]
Shields, P.C.
Entropy and prefixes.
The Annals of Probability, 20, no 1:403--409, 1992.
[127]
Shields, P.C.
The Ergodic Theory of Discrete Sample Paths
American Mathematical Society, 1996.
[128]
Szpankowski, W.
On the Height of Digital Trees and Related Problems
Algorithmica, 6:256--277, 1991.
[129]
Szpankowski, W.
Asymptotic properties of data compression and suffix trees
IEEE Trans. Information Theory, 39(5):1647--1659, 1993.
[130]
Vallois, Pierre and Tapiero, Charles S.
Memory-based persistence in a counting random walk process
Phys. A., 386(1):303--307, 2007.
[131]
Vallois, Pierre and Tapiero, Charles S.
A claims persistence process and insurance
Insurance Math. Econom., 44(3):367--373, 2009.
[132]
Claire Tauvel
Optimisation stochastique à grande échelle
Phd thesis, Université Joseph Fourier, 2008.
[133]
Cénac, P.
Test on the Structure of Biological Sequences via Chaos Game Representation
Statistical Applications in Genetics and Molecular Biology, 4(1), 2005. 34 pages.
[134]
Thangavelu, K.
Quantile estimation based on the almost sure central limit theorem
Phd thesis, Georg–August University of Göttingen, Göttingen, Germany., 2005.
[135]
Cénac, P.
Etude statistique de séquences biologiques et convergence de martingales
Phd thesis, Université Toulouse III, 2006.
[136]
Vardi, Yehuda and Zhang, Cun-Hui
The multivariate $L\sb 1$-median and associated data depth
Proc. Natl. Acad. Sci. USA, 97(4):1423--1426 (electronic), 2000.
[137]
Wand, M. P. and Jones, M. C.
Kernel smoothing
Chapman and Hall Ltd., London, 1995.
[138]
Wang, X-J.
Statistical physics of temporal intermittency
Physical Review A, 40, no 11:6647-6661, 1989.
[139]
Wei, C.Z.
Adaptative prediction by least squares predictors in stochastic regression models with applications to time series
The Annals of Statistics, 15(4):1667-1682, 1987.
[140]
Wei, C.Z.
Asymptotic properties of least-squares estimates in stochastic regression models
The Annals of Statistics, 13(4):1498-1508, 1985".
[141]
Wei, C. Z. and Winnicki, J.
Estimation of the means in the branching process with immigration
Ann. Statist., 18(4):1757--1773, 1990.
[142]
P. Weiner
Linear pattern matching algorithm
14th Annual IEEE Symposium on Switching and Automata Theory, , Washington, DC, 1973.
[143]
Williams, D.
Probability with martingales
Cambridge University Press, Cambridge, 1991.
[144]
Wyner, A.D. and Ziv, J
Some Asymptotic Properties of the Entropy of a Stationary Ergodic Data Source with Applications to Data Compression
IEEE Transactions on Information Theory, 35, no 6:1250--1258, 1989.
[145]
Yuditski, A. B. and Nazin, A. V. and Tsybakov, A. B. and Vayatis, N.
Recursive aggregation of estimators by the mirror descent method with averaging
Problemy Peredachi Informatsii, 41(4):78--96, 2005.
[146]
Ziv, J. and Lempel, A.
A universal algorithm for sequential data compression
IEEE Trans. Information Theory, IT-23(3):337--343, 1977.
[147]
Benveniste, A. and Métivier, M. and Priouret, P.
Adaptive Algorithms and Stochastic Approximations
Springer-Verlag, New York, 1990.
[148]
Eckstein, Eugene C. and Goldstein, Jerome A. and Leggas, Mark
The mathematics of suspensions: Kac walks and asymptotic analyticity
Proceedings of the Fourth Mississippi State Conference on Difference Equations and Computational Simulations (1999), , San Marcos, TX, 2000.
[149]
Es-Sebaiy, K
Berry-Esseen bounds for the least squares estimator for discretely observed fractional Ornstein-Uhlenbeck processes.
Submitted for publication, http://arxiv.org/abs/1202.5061.
[150]
Renshaw, Eric and Henderson, Robin
The correlated random walk
J. Appl. Probab., 18(2):403--414, 1981.
[151]
Cénac, P
Apprivoiser le hasard ou comment les martingales mesurent la taille des dictionnaires en arbres
UB Sciences, 2009.
[152]
Weiss, George H.
Some applications of persistent random walks and the telegrapher's equation
Phys. A, 311(3-4):381--410, 2002.
[153]
Weiss, George H.
Aspects and applications of the random walk
North-Holland Publishing Co., Amsterdam, 1994.
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